The 'confluent Heun equation' is derived from the Heun equation by the coincidence of singularities at \(z=a\)  and \(z=\infty \) . The general confleunce process is discussed in details in Ince [1]}. Also derivation of the confluent Heun equation (CHE) is given as an illustration in Ref. [2]}. The most general form of CHE is expressed as;
\(\psi ^{\prime \prime }(z)+\bigg (\sum _{i=1}^{2}\frac{A_{i}}{z-z_{i}}+\sum _{j=1}^{2}\frac{E_{3j}}{(z-z_{3})^{j}}\bigg )\psi ^{\prime }(z)+\nonumber \\\bigg (\sum _{i=1}^{2}\frac{C_{i}}{z-z_{i}}+\sum _{i=1}^{2}\frac{B_{i}}{(z-z_{i})^{2}}+\sum _{j=1}^{4}\frac{D_{3j}}{(z-z_{3})^{j}}\bigg )\psi (z)=0\) 
